Abstract. The existing relational network Data Envelopment Analysis (DEA) models evaluate the performance of Decision Making Units (DMUs) with precise data. Whereas, in the real-world applications, there are many Supply Chain (SC) networks with imprecise and vague gures. This paper develops a relational network DEA model for evaluating the performance of supply chains with fuzzy numbers. The proposed fuzzy model is capable of evaluating the performance of all kinds of network structures. A pair of twolevel mathematical programs is utilized to convert the fuzzy relational network DEA to a conventional crisp one. For this purpose, the upper and lower bounds of the e ciencies are calculated by -cut concept. The proposed model is implemented using actual data from the supply chain of an international shipping company in Iran.

Data Envelopment Analysis (DEA) is a nonparametric method for identifying sources and estimating the mount of inefficiencies contained in inputs and outputs produced by Decision Making Units (DMUs). DEA requires that the data for all inputs and outputs should be known exactly, but under many qualifications, exact data are inadequate to model real-life situations. So these data may have different structures such as bounded data, interval data, and fuzzy data. Moreover, the main assumption in all DEA is that input and output values are positive, but we confront many cases that discount this condition producing negative data. The purpose of this paper is to compute efficiency for DMUs, which permits the presence of intervals which can take both negative and positive values.

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